Reland "Use BLAS.trsm! instead of LAPACK.trtrs! in left-triangular solves"

[dkarrasch]

This was the conclusion from #1405. This time, we should try to identify ill-posed benchmark problems.

Fixes #1405.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 94.33%. Comparing base (f25276e) to head (aa1bbee).
⚠️ Report is 31 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1529      +/-   ##
==========================================
- Coverage   94.37%   94.33%   -0.04%     
==========================================
  Files          35       35              
  Lines       16050    16059       +9     
==========================================
+ Hits        15147    15150       +3     
- Misses        903      909       +6     

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[dkarrasch]

I couldn't get the BenchmarkSuite running locally. Would anyone volunteer to try this out? The issue must be with the benchmarks, not with this PR. What I find strange is that the zero pivot check is included in LAPACK, so if that's an issue for one of the benchmark problems, then it should come up with the previous call as well...

[ViralBShah]

Is it BLASBenchmarksCPU.jl or some other repo?

[dkarrasch]

I don't know. Somebody said that the benchmarks were failing after the original PR, and reverted it. I never came across the actual error, but, as I said, I also couldn't get the benchmarks running locally. But I thought it was the "normal" benchmark suite.